Determine all possible real values of m such that:
3m * 21m2 = 21
The exact solution is a bit ugly, but it can be a little neater if we let a=log_3(21)=log(21)/log(3)
Taking the base 3 logarithm of both sides yields
m + am^2 = a
Which is a quadratic in m. The solutions are then given by
m = (-1 +/1 sqrt(1+4a^2))/(2a)
I don't think this can be simplified much. The approximate solutions are
m={-1.197, 0.836}
Checking my math
https://www.desmos.com/calculator/eunb9djkzt
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Posted by Jer
on 2023-11-01 08:52:42 |
Solution
